Numerical simulation of flow over an airfoil for small wind turbines using the \(\gamma - {\text{Re}}_{\theta }\) model

Int J Energy Environ Eng (2015) 6:419–429 DOI 10.1007/s40095-015-0188-7 Numerical simulation of flow over an airfoil for small wind turbines using the c  Reh model Haseeb Shah1 • Sathyajith Mathew1 • Chee Ming Lim1 Received: 1 July 2014 / Accepted: 31 July 2015 / Published online: 23 October 2015 Ó The Author(s) 2015. This article is published with open access at Springerlink.com Abstract The mechanism of the laminar separation bubble and the laminar-turbulent transition over the airfoil UBD5494 is simulated in ANSYS-FLUENT using the transition gamma  Reh model at Reynolds number 6 9 104, 1 9 105, 1.5 9 105, 2 9 105 and 3 9 105. Modified constants of the Reynolds momentum thickness are incorporated in the model. The aerodynamic performance of the airfoil is also examined against the flow behaviour. Simulation results show that with the increase in angle of attack, laminar separation bubble moves towards the leading edge and at the same time contracts in size. It starts to expand after reaching the foremost point of the leading edge and then bursts, resulting in flow turbulence and stall. With decreasing Re, the size of the laminar separation bubble is found to be increasing and its progress towards the leading edge is noticed to be slower. The numerical results also indicated that UBD5494 airfoil has enhanced lift-to-drag ratio and desirable stall characteristics which are distinctively advantageous for the better performance of small wind turbine rotors. Keywords Airfoil  Low Reynolds number flows  Laminar separation bubble  Small wind turbine & Haseeb Shah Sathyajith Mathew Chee Ming Lim 1 Centre for Advanced Materials and Energy Sciences, Universiti Brunei Darussalam, Jalan Tungku link, Bandar Seri Begawan BE1410, Brunei Darussalam List of symbols Re Reynolds number, ðRe ¼ qL Uref =lÞ c Intermittency n Boundary-layer co-ordinate ue Edge velocity H Shape factor ðH ¼ d =hÞ h The boundary-layer momentum thickness    2 Cf Skin friction coefficient, Cf ¼ s 0:5 qUref Boundary-layer displacement thickness d 2 que h Total momentum defect a Angle of attack (degree) x/C Axial distance over airfoil axial chord (m) l Molecular viscosity (Pa.s) lt Eddy viscosity (Pa.s) X Absolute value of vorticity Reh Momentum thickness Reynolds number Rehc Critical Reynolds number Reht Transition onset momentum thickness Reynolds number, ðReht ¼ qht UO =lÞ ~ ht Local transition onset momentum thickness Re Reynolds number ReV Strain rate (vorticity) Reynolds number x Specific turbulence dissipation rate (m2 s-1) k Turbulent kinetic energy (J kg-1) S Strain rate (s-1) y Distance from to nearest wall (m) y? Distance in wall coordinates Cl Coefficient of lift, (Cl = L/0.5qU2S*) Cd Coefficient of drag, (Cd = D/0.5qU2S*) Clmax Maximum value of coefficient of lift Cp Coefficient of pressure, (CP = P/0.5qU2) L/D Lift-to-drag ratio, (L/D = Cl/Cd) L Lift (N m-1) D Drag (N m-1) 123 420 q L Uref U UO S Int J Energy Environ Eng (2015) 6:419–429 Density (Kg m-3) Characteristic linear dimension (m) Inlet reference velocity (m s-1) Local velocity (m s-1) Local free stream velocity (m s-1) Wing span area Subscripts t Transition onset s Streamline Abbreviations CFD Computational fluid dynamics LSB Laminar separation bubble 2D Two dimensional SIMPLE Semi-implicit method for pressure-linked equations HAWTs Horizontal axis wind turbines VAWTs Vertical axis wind turbines SWTs Small wind turbines RANS Reynolds averaged Navier–Stokes TKE Turbulent kinetic energy X-foil A post-design viscous/inviscid analysis tool Introduction With the increasing world’s energy requirement and growing environmental concerns, renewable energy resources like wind, solar, biomass, etc. are expected to significantly supplement the expensive and depleting fossil fuels. Among these, wind power with its cumulative installed capacity of nearly 31 9 105 MW by 2013 has alone contributed about 2.5 % of worldwide electricity demand [1]. It is expected to further grow and reach up to 8–12 % by 2020 [1]. In contrast to large wind power sector, small wind industry is also growing at a fast rate. With the growth rate of nearly 35 % annually, total installations of small wind turbines (SWTs) in 2015 are projected to be approximately 400 MW [3]. These installations include both the Horizontal and Vertical axis type wind turbines (HAWTs and VAWTs). From 2015 to 2020, with 1000 MW of newly installed capacity added annually, a steady growth rate of 20 % is forecasted, leading to a cumulative installed capacity of 5 GW by 2020 [3]. SWTs are defined as systems with rotor swept area not more than 200 m2 with an equivalent power of about 50 kW [2]. Applications of such small wind systems include, but are not limited to the sectors of water pumping, telecommunication power supply, irrigation, homes and small industries [4]. Installations of such small systems are often based on the places where the power is required and 123 not necessarily on the strength of the wind [5, 6]. Additionally, for simplicity reasons, they are designed to selfstart and work as stand alone or in connection with microgrids [5, 6]. Moreover, due to the small blade size and the low wind speed working conditions, airfoil device employed along the small HAWT blades operates at low Reynolds number (Re) from hub to tip [6]. The complex nature of flow about the blades in low Re warrants for a careful and ‘clever’ selection of the airfoil profiles in the SWT design process [7]. Typical airfoils designed for high Re, such as NACA airfoil series, are reported to underperform under such low Re conditions and consequently degrade the wind turbine performance [7, 8]. Alongside, airfoils designed for low Re specifically for small HAWTs are found to be limited in the literature [7–17]. While developing small HAWTs for specific applications, the initial aerodynamic performance of an airfoil is generally investigated experimentally in a wind tunnel. At low Re, such wind tunnel measurements are reported to be challenging due to the requirement of higher level of accuracy in equipments for correct modelling of the flow around the airfoils [18]. These include the modelling of the laminar separation bubble (LSB) and the flow behaviour over airfoil’s surface. For example, under the same testing conditions, a difference of 50 % in drag coefficient measurement of Wortmann FX63-137 airfoil was reported under three different testing facilities [19]. On the other hand, with modern computational power, it is now possible to simulate transitions and turbulent flows with Reynolds averaged Navier–Stokes (RANS)based computational fluid dynamics (CFD) models with lower risks of inaccuracy [19, 20]. Yet, a precise computational study requires proper modelling and interpretation of the transition physics. This paper is formulated by keeping such level of accuracy in the simulation and modelling in mind. Moreover, this paper is a first computational effort towards the understanding of (...truncated)